In some proposed wireless systems, data is wirelessly transmitted block by block with a separation interval between successive blocks. This property permits the application of joint detection (JD) in receivers to suppress the inter-symbol interference (ISI) and multiple-access interference (MAI). Single user detectors (SUDs) are used to estimate data of signals that go through a single downlink channel. An advantage of the SUD is that it can be implemented efficiently by fast Fourier transform (FFT), based on the rationale that a square Toeplitz matrix can be approximated as a circulant counterpart of the same size.
When Toeplitz matrices are shortened along their longer dimensions to square matrices and replaced with their circulant counterparts, an approximation error is introduced. This error is most prevalent in the head and tail portions of the matrix. In many systems, the data associated with the head and tail portions carries system information required by the receivers, such as power control bits and the transport format combination indicator (TFCI) in the proposed third generation partnership project (3GPP) wideband code division multiple access (WCDMA) time division duplex (TDD) system. It is desirable to enhance data estimation in such systems.